Digital Twin-Based Air Defense Operational Coordination Method and System

Abstract

This invention belongs to the field of digital twin technology, specifically relating to a collaborative air defense combat method and system based on digital twins, including the following steps: S1, acquiring battlefield situation data; constructing a three-dimensional state gradient tensor field based on the battlefield situation data; when the maximum eigenvalue of the state gradient tensor field within any spatial hexahedron exceeds a preset splitting threshold, asymmetricly splitting the spatial hexahedron along the eigenvector direction corresponding to the maximum eigenvalue to obtain a set of heterogeneous combat tiles; S2, constructing a combat digital twin based on the heterogeneous combat tiles, and mapping the battlefield situation data into the combat digital twin; obtaining the spatiotemporal effectiveness of each heterogeneous combat tile based on the kinematic parameters of the target within the heterogeneous combat tiles and the reciprocal of the predicted information entropy increase rate calculated by the sensor refresh cycle. This invention can improve the scientific nature and practical effectiveness of collaborative air defense combat schemes.

Description

Technical Field

[0001] This invention belongs to the field of digital twin technology, specifically relating to a collaborative method and system for air defense operations based on digital twins. Background Technology

[0002] Modern warfare presents numerous, fast-moving, and highly mobile targets in a complex electromagnetic environment, posing a significant challenge to traditional single-platform combat models. To counter high-level air threats, networking geographically dispersed sensors and weapon systems to form a unified, integrated air defense view has become a key development direction. Cooperative engagement capabilities, through real-time data sharing, enable the entire operational network to operate as a unified whole, thereby improving interception efficiency and survivability.

[0003] Air defense command systems typically employ threat assessment and weapon allocation methods to generate engagement plans. In terms of battlefield situational awareness, fixed grid or voxel-based methods are used to divide the operational space. However, the battlefield situation is constantly changing, and the battlefield area is vast. Excessive computational load cannot cope with the rapid changes in the battlefield, while coordinated operational plans require high precision to suppress the enemy and achieve victory. Balancing computational load and the effectiveness of coordinated operations is a pressing issue that needs to be addressed. Summary of the Invention

[0004] This invention provides a digital twin-based air defense combat coordination method and system to solve the technical problem of balancing computational load and the effectiveness of coordinated operations in the prior art.

[0005] In a first aspect, the present invention provides a collaborative air defense operation method based on digital twins, comprising the following steps:

[0006] S1, acquire battlefield situation data; construct a three-dimensional spatial state gradient tensor field based on the battlefield situation data; when the maximum eigenvalue of the state gradient tensor field in any spatial hexahedron exceeds the preset splitting threshold, perform asymmetric splitting of the spatial hexahedron along the eigenvector direction corresponding to the maximum eigenvalue to obtain a set of heterogeneous combat tiles.

[0007] S2, construct a combat digital twin based on heterogeneous combat tiles, and map battlefield situation data into the combat digital twin; obtain the spatiotemporal effectiveness of each heterogeneous combat tile based on the kinematic parameters of the target within the heterogeneous combat tiles and the reciprocal of the predicted information entropy increase rate calculated by the sensor refresh cycle, and determine the target tiles to be processed in combination with the target threat level;

[0008] S3: For target tiles, generate a cooperative engagement plan in the operational digital twin. Correct the overall interception probability based on the fire channel occupancy rate of the cooperative engagement plan, and evaluate the cooperative engagement plan using a multi-objective function that includes a fire channel saturation term. Simulate the cooperative engagement plan in the operational digital twin, calculate the plume interference probability determined by the minimum distance between trajectories, velocity vector difference, and timing, and update the evaluation value of the cooperative engagement plan by using the plume interference probability to reduce the expected interception probability of the interceptor missile.

[0009] S4: Select the best cooperative combat plan based on the updated evaluation value and output it.

[0010] Furthermore, a three-dimensional state gradient tensor field is constructed based on battlefield situation data. When the maximum eigenvalue of the state gradient tensor field within any spatial hexahedron exceeds a preset splitting threshold, the spatial hexahedron is asymmetrically split along the eigenvector direction corresponding to the maximum eigenvalue to obtain a set of heterogeneous combat tiles, including:

[0011] The three-dimensional space is divided into an initial hexahedral grid, and the velocity field gradient of the target within each hexahedral grid is calculated to form a second-order state gradient tensor.

[0012] Calculate the eigenvalues ​​of the second-order state gradient tensor. When the largest eigenvalue exceeds the splitting threshold, use the eigenvector corresponding to the eigenvalue as the normal vector and define a splitting plane through the geometric center of the hexahedron to cut the hexahedron into two new sub-hexahedrons.

[0013] Furthermore, the spatiotemporal effectiveness of each heterogeneous combat tile is obtained by taking the reciprocal of the predicted information entropy increase rate calculated based on the kinematic parameters of the target within the heterogeneous combat tile and the sensor refresh cycle, including:

[0014] For each target within the heterogeneous combat tile, a Kalman filter state transition model is constructed using the target's current velocity and acceleration to predict the position covariance matrix up to the next sensor refresh cycle.

[0015] Calculate the determinant of the covariance matrix, and take the logarithm of the determinant as the predicted information entropy of the target;

[0016] Calculate the difference between the predicted information entropy and the information entropy at the current moment to obtain the target's predicted information entropy increase rate;

[0017] The maximum predicted information entropy increase rate among all targets within a heterogeneous combat tile is selected, and the reciprocal of the maximum predicted information entropy increase rate is taken as the spatiotemporal effectiveness of the heterogeneous combat tile.

[0018] Furthermore, the overall interception probability is corrected based on the fire channel occupancy rate of the coordinated engagement plan, and a multi-objective function including a fire channel saturation term is used to evaluate the coordinated engagement plan, including:

[0019] The evaluation function of the coordinated engagement plan is ;

[0020] in, The evaluation function for the coordinated engagement plan. It is the product of the success probabilities of all independent interception events in the coordinated engagement plan. For resource consumption cost; S is the fire channel saturation term, calculated using the following formula: ,in The number of fire control channels occupied by the coordinated combat plan. This represents the total number of fire control channels in the system. and This is the preset penalty coefficient.

[0021] Furthermore, the plume interference probability, determined by the minimum distance between trajectories, velocity vector difference, and timing, is calculated. The expected interception probability of the interceptor missile after the plume interference probability is reduced is then used to update the assessment values ​​of the cooperative engagement plan, including:

[0022] For two interceptions that are sequentially adjacent, the trajectories are extrapolated in the digital twin, and the shortest spatial distance between the two trajectories is calculated. and the velocity vectors at their respective interception points and ;

[0023] When the subsequent interception time is later than the preceding interception time, calculate the plume interference probability. :

[0024] Where K and D are preset constants, and The constraint is within the interval [0,1].

[0025] The expected interception probability of the follow-up interceptor missile Updated to ,in This is the corrected interception probability.

[0026] Furthermore, based on the target threat level, the target tiles to be processed are determined, including:

[0027] Based on the distance, flight speed, and target type of targets within heterogeneous combat tiles from our defensive strongholds, normalized threat level values ​​are assigned to the heterogeneous combat tiles. ;

[0028] Spatiotemporal validity Threat Level Value Perform a weighted summation to obtain the processing priority of heterogeneous combat tiles. ,in and Preset weighting coefficients;

[0029] Select processing priority At least one heterogeneous combat tile is selected as the target tile to be processed.

[0030] Secondly, the present invention provides an air defense combat coordination system based on digital twins, comprising the following modules:

[0031] The segmentation module is used to acquire battlefield situation data; based on the battlefield situation data, a three-dimensional spatial state gradient tensor field is constructed. When the maximum eigenvalue of the state gradient tensor field in any spatial hexahedron exceeds the preset splitting threshold, the spatial hexahedron is asymmetrically split along the eigenvector direction corresponding to the maximum eigenvalue to obtain a set of heterogeneous combat tiles.

[0032] The target tile acquisition module is used to construct a combat digital twin based on heterogeneous combat tiles and map battlefield situation data into the combat digital twin. The spatiotemporal effectiveness of each heterogeneous combat tile is obtained based on the kinematic parameters of the target within the heterogeneous combat tile and the reciprocal of the predicted information entropy increase rate calculated by the sensor refresh cycle. The target tile to be processed is determined in combination with the target threat level.

[0033] The tile evaluation module is used to generate a cooperative engagement plan in the operational digital twin for target tiles. It corrects the overall interception probability based on the fire channel occupancy rate of the cooperative engagement plan and evaluates the cooperative engagement plan using a multi-objective function that includes a fire channel saturation term. The module also simulates the cooperative engagement plan in the operational digital twin, calculates the plume interference probability determined by the minimum distance between trajectories, velocity vector difference, and timing, and updates the evaluation value of the cooperative engagement plan by using the expected interception probability of the interceptor missile after the plume interference probability is reduced.

[0034] The engagement plan output module selects and outputs the best cooperative engagement plan based on the updated evaluation values.

[0035] Furthermore, a three-dimensional state gradient tensor field is constructed based on battlefield situation data. When the maximum eigenvalue of the state gradient tensor field within any spatial hexahedron exceeds a preset splitting threshold, the spatial hexahedron is asymmetrically split along the eigenvector direction corresponding to the maximum eigenvalue to obtain a set of heterogeneous combat tiles, including:

[0036] The three-dimensional space is divided into an initial hexahedral grid, and the velocity field gradient of the target within each hexahedral grid is calculated to form a second-order state gradient tensor.

[0037] Calculate the eigenvalues ​​of the second-order state gradient tensor. When the largest eigenvalue exceeds the splitting threshold, use the eigenvector corresponding to the eigenvalue as the normal vector and define a splitting plane through the geometric center of the hexahedron to cut the hexahedron into two new sub-hexahedrons.

[0038] Furthermore, the spatiotemporal effectiveness of each heterogeneous combat tile is obtained by taking the reciprocal of the predicted information entropy increase rate calculated based on the kinematic parameters of the target within the heterogeneous combat tile and the sensor refresh cycle, including:

[0039] For each target within the heterogeneous combat tile, a Kalman filter state transition model is constructed using the target's current velocity and acceleration to predict the position covariance matrix up to the next sensor refresh cycle.

[0040] Calculate the determinant of the covariance matrix, and take the logarithm of the determinant as the predicted information entropy of the target;

[0041] Calculate the difference between the predicted information entropy and the information entropy at the current moment to obtain the target's predicted information entropy increase rate;

[0042] The maximum predicted information entropy increase rate among all targets within a heterogeneous combat tile is selected, and the reciprocal of the maximum predicted information entropy increase rate is taken as the spatiotemporal effectiveness of the heterogeneous combat tile.

[0043] Furthermore, the overall interception probability is corrected based on the fire channel occupancy rate of the coordinated engagement plan, and a multi-objective function including a fire channel saturation term is used to evaluate the coordinated engagement plan, including:

[0044] The evaluation function of the coordinated engagement plan is ;

[0045] in, The evaluation function for the coordinated engagement plan. It is the product of the success probabilities of all independent interception events in the coordinated engagement plan. For resource consumption cost; S is the fire channel saturation term, calculated using the following formula: ,in The number of fire control channels occupied by the coordinated combat plan. This represents the total number of fire control channels in the system. and This is the preset penalty coefficient.

[0046] The beneficial effects are as follows: This invention generates heterogeneous combat tiles that reflect the density distribution of the battlefield situation by introducing an asymmetric spatial splitting technique based on the state gradient tensor field. It incorporates a nonlinear penalty term for fire channel saturation into the evaluation function, ensuring that the generated cooperative engagement plan fully considers the actual carrying capacity of the weapon system and is closer to real combat. Furthermore, it quantitatively models and extrapolates the plume interference effect during multi-missile cooperative interception, improving the accuracy of predicting combat outcomes under saturation attack scenarios by reducing the expected probability of subsequent interceptor missiles. In summary, this invention can improve the scientific rigor and practical effectiveness of air defense cooperative engagement schemes. Attached Figure Description

[0047] Figure 1 This is a flowchart of a collaborative air defense operation method based on digital twins. Detailed Implementation

[0048] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0049] An embodiment of the air defense combat coordination method based on digital twin provided by this invention:

[0050] like Figure 1 As shown, the air defense combat coordination method based on digital twins includes the following steps:

[0051] S1, acquire battlefield situation data; construct a three-dimensional state gradient tensor field based on the battlefield situation data; when the maximum eigenvalue of the state gradient tensor field in any spatial hexahedron exceeds the preset splitting threshold, perform asymmetric splitting of the spatial hexahedron along the eigenvector direction corresponding to the maximum eigenvalue to obtain a set of heterogeneous combat tiles.

[0052] The battlefield situation changes in real time. Data from multiple long-range early warning radars, fire control radars, optoelectronic reconnaissance equipment, and electronic support systems is received in real time through the integrated theater command information system. This data undergoes coordinate unification and time synchronization processing to form a structured dataset containing information on the three-dimensional position, velocity, acceleration, radar cross-section, and threat level of all aerial targets. It also includes the position, ammunition quantity, and equipment status of friendly air defense fire units, forming a unified battlefield situation map. The entire combat airspace is initialized as a large hexahedron. A scalar potential field is defined based on the battlefield situation data. Optionally, the potential field value at any point in space is equal to the sum of the threat contributions of all enemy targets, with the magnitude of the threat contribution being directly proportional to the target threat level and inversely proportional to the square of the distance. The second-order partial derivatives of the potential field value at the center point of each hexahedron are calculated, forming a 3×3 Hessian matrix, which is the state gradient tensor. Eigenvalue decomposition is performed on the state gradient tensor to obtain three eigenvalues ​​and corresponding eigenvectors. The maximum eigenvalue is compared with a preset splitting threshold. If it exceeds the splitting threshold, a plane is generated with the center of the hexahedron as the origin and the eigenvector corresponding to the maximum eigenvalue as the normal vector, cutting the hexahedron into two new sub-hexahedrons. The above process is repeated recursively until the maximum eigenvalue of all hexahedrons is no greater than the splitting threshold. The resulting set of all terminal hexahedrons constitutes the heterogeneous combat tile set.

[0053] In an optional embodiment, a three-dimensional state gradient tensor field is constructed based on battlefield situation data. When the maximum eigenvalue of the state gradient tensor field within any spatial hexahedron exceeds a preset splitting threshold, the spatial hexahedron is asymmetrically split along the eigenvector direction corresponding to the maximum eigenvalue to obtain a set of heterogeneous combat tiles, including:

[0054] The three-dimensional space is divided into an initial hexahedral grid, and the velocity field gradient of the target within each hexahedral grid is calculated to form a second-order state gradient tensor.

[0055] Calculate the eigenvalues ​​of the second-order state gradient tensor. When the largest eigenvalue exceeds the splitting threshold, use the eigenvector corresponding to the eigenvalue as the normal vector and define a splitting plane through the geometric center of the hexahedron to cut the hexahedron into two new sub-hexahedrons.

[0056] A set of enemy targets with all three-dimensional spatial coordinates located inside a hexahedron is obtained, and the current position and velocity vector data of each target are extracted. Discrete kinematic data points are used as samples of a local continuous velocity field. A local linear mapping model from position vector to velocity vector is established using a numerical fitting method, such as multiple linear regression based on the least squares criterion. The local linear mapping model solves for an optimal 3x3 second-order state gradient tensor, such that the linear velocity field defined by the second-order state gradient tensor can approximate the true velocity distribution of all sampled targets within the hexahedron to the greatest extent. The second-order state gradient tensor is the desired velocity field gradient, and its nine components represent the rate of change of the velocity vector in the local space along the three coordinate axes.

[0057] If the preset splitting threshold λ split The value is 0.5. Since 1.2 is greater than 0.5, we obtain... λ max The corresponding feature vector V max The eigenvectors indicate the direction of the fastest change in velocity. Taking the geometric center of the hexahedron as the origin, and V... max A splitting plane is generated along the normal direction. This splitting plane asymmetrically cuts the original hexahedron, for example, 10km×10km×3km, into two new sub-hexahedrons of different volumes. The mesh remains sparse in stable regions, while it is refined in densely populated or highly maneuverable regions, improving computational efficiency while maintaining accuracy.

[0058] S2, constructs a combat digital twin based on heterogeneous combat tiles, and maps battlefield situation data into the combat digital twin; the spatiotemporal effectiveness of each heterogeneous combat tile is obtained based on the kinematic parameters of the target within the heterogeneous combat tile and the reciprocal of the predicted information entropy increase rate calculated by the sensor refresh cycle, and the target tile to be processed is determined in combination with the target threat level.

[0059] In a virtual computing environment, a digital model of the battlefield space is created using the geometric structure of heterogeneous combat tiles as the basic mesh framework in three-dimensional space. Specifically, the set of all heterogeneous combat tiles generated after splitting the battlefield space through a state gradient tensor field serves as the geometric foundation of the digital twin world. Various combat entities contained in the real-time battlefield situation data, including but not limited to enemy incoming targets, friendly radars, missile launch units, command and control nodes, and protected assets, are instantiated into virtual objects within the corresponding heterogeneous combat tiles in the digital twin based on four-dimensional spatiotemporal coordinates. Each virtual object is assigned performance parameters, physical models, behavioral logic, and interaction rules, such as the radar cross-section model of the target and the flight dynamics and damage model of the interceptor missile. This constructs a digital mirror in the virtual space that is consistent with and synchronized in real time with the physical battlefield in terms of spatial structure, entity state, and operational rules.

[0060] Extract the current state covariance matrix of all targets in the heterogeneous combat tiles containing the target. Using the target's kinematic model (including but not limited to uniform velocity or uniform acceleration models), predict the target's state covariance matrix at the end of the next sensor refresh cycle. The information entropy increase rate is approximated by calculating the ratio of the determinant of the predicted state covariance matrix to the determinant of the current state covariance matrix. In one embodiment, spatiotemporal effectiveness is the reciprocal of this ratio. Calculate the comprehensive threat value based on factors such as the target's distance from friendly protected assets and its flight speed within the heterogeneous combat tiles. Combine the comprehensive threat value with spatiotemporal effectiveness in a weighted manner to form a processing priority score for the heterogeneous combat tiles. Select the heterogeneous combat tiles with the highest scores as the target tiles to be processed.

[0061] In an optional embodiment, the spatiotemporal effectiveness of each heterogeneous combat tile is obtained based on the reciprocal of the predicted information entropy increase rate calculated using the kinematic parameters of the target within the heterogeneous combat tile and the sensor refresh cycle, including:

[0062] For each target within the heterogeneous combat tile, a Kalman filter state transition model is constructed using the target's current velocity and acceleration to predict the position covariance matrix up to the next sensor refresh cycle.

[0063] Calculate the determinant of the covariance matrix, and take the logarithm of the determinant as the predicted information entropy of the target;

[0064] Calculate the difference between the predicted information entropy and the information entropy at the current moment to obtain the target's predicted information entropy increase rate;

[0065] The maximum predicted information entropy increase rate among all targets within a heterogeneous combat tile is selected, and the reciprocal of the maximum predicted information entropy increase rate is taken as the spatiotemporal effectiveness of the heterogeneous combat tile.

[0066] Spatiotemporal effectiveness measures the predictability of a target's state within a heterogeneous operational tile. A lower value indicates a faster increase in uncertainty, requiring greater priority. For example, a heterogeneous operational tile might contain a high-speed maneuvering missile A and a reconnaissance aircraft B flying at a constant speed in a straight line, with a radar refresh rate of 1 second. At the current moment, the determinant of the position uncertainty covariance matrix for missile A is 4, and its information entropy is the natural logarithm of 4, approximately 1.39. Based on its speed of 1500 meters per second and an acceleration of 5g, the determinant of the covariance matrix is ​​predicted to increase to 25 after 1 second, with a prediction information entropy of the natural logarithm of 25, approximately 3.22.

[0067] The predicted information entropy increase rate of missile A is 3.22 - 1.39 = 1.83. Meanwhile, due to flight stability, the determinant of the covariance matrix of reconnaissance aircraft B increases from 2 to 2.5, with an information entropy increase rate of 0.22. The larger of the two, 1.83, is selected as the representative value for this heterogeneous combat tile. The spatiotemporal effectiveness of the heterogeneous combat tile is approximately 0.55.

[0068] In an optional embodiment, determining the target tile to be processed based on the target threat level includes:

[0069] Based on the distance, flight speed, and target type of targets within heterogeneous combat tiles from our defensive strongholds, normalized threat level values ​​are assigned to the heterogeneous combat tiles. ;

[0070] Spatiotemporal validity Threat Level Value Perform a weighted summation to obtain the processing priority of heterogeneous combat tiles. ,in and Preset weighting coefficients;

[0071] Select processing priority At least one heterogeneous combat tile is selected as the target tile to be processed.

[0072] Assuming weight coefficients It is 0.3. The target value is 0.7. There are two target tiles to be processed: tile A and tile B. Tile A contains a ballistic missile, which is only 60 kilometers away from the defensive position and has an extremely high speed. After calculation and normalization, it is 0.95. Due to the ballistic stability, state prediction is relatively easy, and the spatiotemporal effectiveness is good. The threat level is relatively high, at 0.8. There are two fighter jets performing complex formation maneuvers within target tile B, at a distance of 200 kilometers, indicating a threat level of [missing information]. The normalized value is 0.6. However, due to its high mobility, its future location is highly uncertain, affecting its spatiotemporal effectiveness. The priority is very low, only 0.2. According to the formula, the processing priority of target tile A is 0.905. The processing priority of target tile B is 0.48. It can be seen that although the state of target tile B is more unstable, the immediate threat of the target within target tile A is much greater. Therefore, its processing priority is much higher than that of target tile B, and resources will be allocated to process target tile A first.

[0073] S3: For the target tile, a cooperative engagement plan is generated in the operational digital twin. The overall interception probability is corrected based on the fire channel occupancy rate of the cooperative engagement plan, and a multi-objective function including the fire channel saturation term is used to evaluate the cooperative engagement plan. The cooperative engagement plan is then simulated in the operational digital twin, and the plume interference probability determined by the minimum distance between trajectories, velocity vector difference, and timing is calculated. The expected interception probability of the interceptor missile after the plume interference probability is reduced is used to update the evaluation value of the cooperative engagement plan.

[0074] For all targets within the target tile, all available fire units are invoked, and algorithms such as simulated annealing are used to generate multiple weapon-target allocation combinations, i.e., coordinated engagement plans. The initial evaluation value of each coordinated engagement plan is the sum of the expected interception probabilities of all assigned tasks. Further, a saturation term is calculated. For a given coordinated engagement plan, the number of interceptor missiles allocated to the same guidance radar or launcher, i.e., the number of fire channel occupancy, is counted and divided by the maximum number of tasks it can handle simultaneously to obtain the fire channel occupancy rate. An S-shaped penalty function is preferably used; when the fire channel occupancy rate is low, the penalty factor is close to 1, and when the fire channel occupancy rate approaches 100%, the penalty factor rapidly decreases to near zero. The initial evaluation value is multiplied by the penalty factor to obtain the corrected evaluation value.

[0075] A rapid dynamic simulation is performed for each coordinated engagement scenario. In the simulation, the flight trajectories of any two interceptor missiles launched sequentially and targeting close targets are parameterized. The exhaust plume of the first interceptor missile is modeled as a cone expanding over time. The spatiotemporal geometric relationship between the trajectory of the subsequent interceptor missile and this cone is calculated to determine the minimum distance between the trajectories, the magnitude of the velocity vector difference between the two missiles, and the duration for which the seeker head of the subsequent interceptor missile remains within the exhaust plume region. These three parameters are substituted into a pre-established plume interference probability model, optionally an empirical formula or a lookup table, to output an interference probability value. The original expected interception probability of the subsequent interceptor missile is multiplied by (1 - interference probability value) to obtain a reduced interception probability. The reduced interception probability replaces the original expected interception probability, and the overall evaluation value of the coordinated engagement scenario is recalculated.

[0076] In an optional embodiment, the overall interception probability is corrected based on the fire channel occupancy rate of the coordinated engagement plan, and the coordinated engagement plan is evaluated using a multi-objective function that includes a fire channel saturation term, including:

[0077] The evaluation function of the coordinated engagement plan is ;

[0078] in, It is the product of the success probabilities of all independent interception events in the coordinated engagement plan. For resource consumption cost; S is the fire channel saturation term, calculated using the following formula: ,in The number of fire control channels occupied by the coordinated combat plan. This represents the total number of fire control channels in the system. and This is the preset penalty coefficient.

[0079] Assume a certain defense system has a total of 10 fire control channels, that is The value is 10, with a penalty coefficient of α = 8 and β = 0.7. Plan A involves simultaneously engaging 5 targets, requiring the use of 7 firing channels. With a probability of 7, the overall interception probability is 0.92, and the resource cost is 0.1. According to the formula, the fire channel occupancy rate is 0.7. Since this value does not exceed the threshold β, the fire channel saturation term S is 1, and the evaluation value of Plan A is -0.1. Another plan, Plan B, selects to engage 4 targets, occupying 6 fire channels, with an overall interception probability of 0.88 and a resource cost of 0.08. Its fire channel occupancy rate is 0.6, the fire channel saturation term S is approximately 0.45, and the evaluation value of Plan B is approximately 0.404. Although Plan A has a higher theoretical interception probability, because it saturates the fire channels, its evaluation value is much lower than Plan B, therefore Plan B is more likely to be chosen.

[0080] In an optional embodiment, the plume interference probability, determined by the minimum inter-trajectory distance, velocity vector difference, and timing, is calculated, and the expected interception probability of the interceptor missile after the plume interference probability is reduced is used to update the evaluation value of the cooperative engagement plan, including:

[0081] For two interceptions that are sequentially adjacent, the trajectories are extrapolated in the digital twin, and the shortest spatial distance between the two trajectories is calculated. and the velocity vectors at their respective interception points and ;

[0082] When the subsequent interception time is later than the preceding interception time, calculate the plume interference probability. :

[0083] Where K and D are preset constants, and The constraint is within the interval [0,1].

[0084] The expected interception probability of the follow-up interceptor missile Updated to .

[0085] The plume interference model used in this invention is a mathematical model for quantitatively calculating the probability that the high-temperature exhaust plume of the engine of the preceding interceptor missile will interfere with the infrared or radio frequency seeker of the following interceptor missile in two interception missions that are sequentially adjacent. This mathematical model is a formula that integrates spatial, temporal, and kinematic factors: an exponential decay term characterizing spatial proximity, the value of which varies with the shortest spatial distance between the trajectories of the two interceptor missiles. The exponential decrease in the value of the plume energy density reflects the attenuation of the plume energy density with distance diffusion; a direction cosine term characterizing the geometric alignment is calculated by determining the velocity vectors of the two interceptor missiles at their respective interception points. and The normalized dot product is obtained, ensuring that the jamming effect is only calculated when the flight path of the follow-up interceptor is similar to that of the lead interceptor and there is a possibility of crossing the plume region; and an empirical constant K related to the interceptor's fuel type, engine parameters, and atmospheric environment. This ensures that a significant jamming probability is calculated only when specific conditions are met in the three dimensions of timing, space, and direction, and the jamming probability is used to calculate the expected interception success rate of the follow-up interceptor.

[0086] For example, one plan is to launch interceptor missile 1 at time T1, and interceptor missile 2 at time T2, two seconds later, to attack two adjacent targets. Digital twin simulation shows the shortest spatial distance between the trajectories of the two interceptor missiles. It is 400 meters.

[0087] At their respective interception points, the velocity vector of interceptor missile 1 and the velocity vector of interceptor missile 2 The plumes are close in direction, with a cosine of 0.9. Assume the plume model constant K is 0.8 and the characteristic attenuation distance D is 800 meters. Calculate the plume interference probability. It is approximately 0.437. If the original expected interception probability of interceptor missile 2... The corrected interception probability is 0.9 after the plume interference probability is reduced. It will decrease by approximately 0.51.

[0088] S4: Select the best cooperative combat plan based on the updated evaluation value and output it.

[0089] All coordinated engagement plans, after plume interference correction, were ranked from highest to lowest based on the final evaluation values. The coordinated engagement plan with the highest evaluation value was selected as the coordinated engagement scheme. The coordinated engagement scheme was then analyzed into a series of specific instructions, each clearly specifying which fire unit, at what time, what type of interceptor missile to launch, and which target number to attack. These instructions were then distributed to the fire control computers of each fire unit via the command and control system to guide their execution of the attack.

[0090] The embodiment of the air defense combat coordination system based on digital twin provided by the present invention includes the following modules:

[0091] The segmentation module is used to acquire battlefield situation data; based on the battlefield situation data, a three-dimensional spatial state gradient tensor field is constructed. When the maximum eigenvalue of the state gradient tensor field in any spatial hexahedron exceeds the preset splitting threshold, the spatial hexahedron is asymmetrically split along the eigenvector direction corresponding to the maximum eigenvalue to obtain a set of heterogeneous combat tiles.

[0092] The target tile acquisition module is used to construct a combat digital twin based on heterogeneous combat tiles and map battlefield situation data into the combat digital twin. The spatiotemporal effectiveness of each heterogeneous combat tile is obtained based on the kinematic parameters of the target within the heterogeneous combat tile and the reciprocal of the predicted information entropy increase rate calculated by the sensor refresh cycle. The target tile to be processed is determined in combination with the target threat level.

[0093] The tile evaluation module is used to generate a cooperative engagement plan in the operational digital twin for target tiles. It corrects the overall interception probability based on the fire channel occupancy rate of the cooperative engagement plan and evaluates the cooperative engagement plan using a multi-objective function that includes a fire channel saturation term. The module also simulates the cooperative engagement plan in the operational digital twin, calculates the plume interference probability determined by the minimum distance between trajectories, velocity vector difference, and timing, and updates the evaluation value of the cooperative engagement plan by using the expected interception probability of the interceptor missile after the plume interference probability is reduced.

[0094] The engagement plan output module selects and outputs the best cooperative engagement plan based on the updated evaluation values.

[0095] The above are all preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Therefore, all equivalent changes made in accordance with the structure, shape and principle of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A collaborative air defense combat method based on digital twins, characterized in that, Includes the following steps: S1, acquire battlefield situation data; construct a three-dimensional state gradient tensor field based on the battlefield situation data; when the maximum eigenvalue of the state gradient tensor field in any spatial hexahedron exceeds the preset splitting threshold, perform asymmetric splitting of the spatial hexahedron along the eigenvector direction corresponding to the maximum eigenvalue to obtain a set of heterogeneous combat tiles. S2 constructs a combat digital twin based on heterogeneous combat tiles and maps battlefield situation data into the combat digital twin; The spatiotemporal effectiveness of each heterogeneous combat tile is obtained by calculating the reciprocal of the predicted information entropy increase rate based on the kinematic parameters of the target within the heterogeneous combat tile and the sensor refresh cycle, and the target tile to be processed is determined by combining the target threat level. S3, for target tiles, generates a cooperative engagement plan in the operational digital twin, adjusts the overall interception probability based on the fire channel occupancy rate of the cooperative engagement plan, and evaluates the cooperative engagement plan using a multi-objective function that includes a fire channel saturation term, including: The evaluation function of the coordinated engagement plan is ; in, The evaluation function for the coordinated engagement plan, It is the product of the success probabilities of all independent interception events in the coordinated engagement plan. For resource consumption cost; S is the fire channel saturation term, calculated using the following formula: ,in The number of fire control channels occupied by the coordinated combat plan. This represents the total number of fire control channels in the system. and This is the preset penalty coefficient; In the operational digital twin, the cooperative engagement plan is simulated, the plume interference probability determined by the minimum distance between trajectories, velocity vector difference and timing is calculated, and the expected interception probability of the interceptor missile after the plume interference probability is reduced is used to update the evaluation value of the cooperative engagement plan. S4: Select the best cooperative combat plan based on the updated evaluation value and output it.

2. The air defense combat coordination method based on digital twins according to claim 1, characterized in that, A three-dimensional state gradient tensor field is constructed based on battlefield situation data. When the maximum eigenvalue of the state gradient tensor field within any spatial hexahedron exceeds a preset splitting threshold, the spatial hexahedron is asymmetrically split along the eigenvector direction corresponding to the maximum eigenvalue to obtain a set of heterogeneous combat tiles, including: The three-dimensional space is divided into an initial hexahedral grid, and the velocity field gradient of the target within each hexahedral grid is calculated to form a second-order state gradient tensor. Calculate the eigenvalues ​​of the second-order state gradient tensor. When the largest eigenvalue exceeds the splitting threshold, use the eigenvector corresponding to the eigenvalue as the normal vector and define a splitting plane through the geometric center of the hexahedron to cut the hexahedron into two new sub-hexahedrons.

3. The air defense combat coordination method based on digital twins according to claim 1, characterized in that, The spatiotemporal effectiveness of each heterogeneous combat tile is obtained by calculating the reciprocal of the predicted information entropy increase rate based on the kinematic parameters of targets within the heterogeneous combat tile and the sensor refresh cycle, including: For each target within the heterogeneous combat tile, a Kalman filter state transition model is constructed using the target's current velocity and acceleration to predict the position covariance matrix up to the next sensor refresh cycle. Calculate the determinant of the covariance matrix, and take the logarithm of the determinant as the predicted information entropy of the target; Calculate the difference between the predicted information entropy and the information entropy at the current moment to obtain the target's predicted information entropy increase rate; The maximum predicted information entropy increase rate among all targets within a heterogeneous combat tile is selected, and the reciprocal of the maximum predicted information entropy increase rate is taken as the spatiotemporal effectiveness of the heterogeneous combat tile.

4. The air defense combat coordination method based on digital twins according to claim 1, characterized in that, Calculate the plume interference probability determined by the minimum inter-trajectory distance, velocity vector difference, and timing, and use the plume interference probability to reduce the expected interception probability of the interceptor missile to update the assessment values ​​of the cooperative engagement plan, including: For two interceptions that are sequentially adjacent, the trajectories are extrapolated in the digital twin, and the shortest spatial distance between the two trajectories is calculated. and the velocity vectors at their respective interception points and ; When the subsequent interception time is later than the preceding interception time, calculate the plume interference probability. : Where K and D are preset constants, and The constraint is within the interval [0,1]. The expected interception probability of the follow-up interceptor missile Updated to ,in This is the corrected interception probability.

5. The air defense combat coordination method based on digital twins according to any one of claims 1-4, characterized in that, The target tiles to be processed are determined based on the target threat level, including: Based on the distance, flight speed, and target type of targets within heterogeneous combat tiles from our defensive strongholds, normalized threat level values ​​are assigned to the heterogeneous combat tiles. ; Spatiotemporal validity Threat Level Value Perform a weighted summation to obtain the processing priority of heterogeneous combat tiles. ,in and Preset weighting coefficients; Select processing priority At least one heterogeneous combat tile is selected as the target tile to be processed.

6. A digital twin-based air defense combat coordination system, characterized in that: Includes the following modules: The segmentation module is used to acquire battlefield situation data; based on the battlefield situation data, a three-dimensional spatial state gradient tensor field is constructed. When the maximum eigenvalue of the state gradient tensor field in any spatial hexahedron exceeds the preset splitting threshold, the spatial hexahedron is asymmetrically split along the eigenvector direction corresponding to the maximum eigenvalue to obtain a set of heterogeneous combat tiles. The target tile acquisition module is used to construct a combat digital twin based on heterogeneous combat tiles and map battlefield situation data into the combat digital twin. The spatiotemporal effectiveness of each heterogeneous combat tile is obtained based on the kinematic parameters of the target within the heterogeneous combat tile and the reciprocal of the predicted information entropy increase rate calculated by the sensor refresh cycle. The target tile to be processed is determined in combination with the target threat level. The tile evaluation module generates a cooperative engagement plan in the operational digital twin for target tiles. It adjusts the overall interception probability based on the fire channel occupancy rate of the cooperative engagement plan and evaluates the plan using a multi-objective function that includes a fire channel saturation term. This evaluation includes: The evaluation function of the coordinated engagement plan is ; in, The evaluation function for the coordinated engagement plan, It is the product of the success probabilities of all independent interception events in the coordinated engagement plan. For resource consumption cost; S is the fire channel saturation term, calculated using the following formula: ,in The number of fire control channels occupied by the coordinated combat plan. This represents the total number of fire control channels in the system. and This is the preset penalty coefficient; In the operational digital twin, the cooperative engagement plan is simulated, the plume interference probability determined by the minimum distance between trajectories, velocity vector difference and timing is calculated, and the expected interception probability of the interceptor missile after the plume interference probability is reduced is used to update the evaluation value of the cooperative engagement plan. The engagement plan output module selects and outputs the best cooperative engagement plan based on the updated evaluation values.

7. The air defense combat coordination system based on digital twins according to claim 6, characterized in that, A three-dimensional state gradient tensor field is constructed based on battlefield situation data. When the maximum eigenvalue of the state gradient tensor field within any spatial hexahedron exceeds a preset splitting threshold, the spatial hexahedron is asymmetrically split along the eigenvector direction corresponding to the maximum eigenvalue to obtain a set of heterogeneous combat tiles, including: The three-dimensional space is divided into an initial hexahedral grid, and the velocity field gradient of the target within each hexahedral grid is calculated to form a second-order state gradient tensor. Calculate the eigenvalues ​​of the second-order state gradient tensor. When the largest eigenvalue exceeds the splitting threshold, use the eigenvector corresponding to the eigenvalue as the normal vector and define a splitting plane through the geometric center of the hexahedron to cut the hexahedron into two new sub-hexahedrons.

8. The air defense combat coordination system based on digital twins according to claim 6, characterized in that, The spatiotemporal effectiveness of each heterogeneous combat tile is obtained by calculating the reciprocal of the predicted information entropy increase rate based on the kinematic parameters of targets within the heterogeneous combat tile and the sensor refresh cycle, including: For each target within the heterogeneous combat tile, a Kalman filter state transition model is constructed using the target's current velocity and acceleration to predict the position covariance matrix up to the next sensor refresh cycle. Calculate the determinant of the covariance matrix, and take the logarithm of the determinant as the predicted information entropy of the target; Calculate the difference between the predicted information entropy and the information entropy at the current moment to obtain the target's predicted information entropy increase rate; The maximum predicted information entropy increase rate among all targets within a heterogeneous combat tile is selected, and the reciprocal of the maximum predicted information entropy increase rate is taken as the spatiotemporal effectiveness of the heterogeneous combat tile.

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